In the past several years it has come to be appreciated that in low Reynolds number flow the nonlinearities provided by non-Newtonian stresses of a complex fluid can provide a richness of dynamical behaviors more commonly associated with high Reynolds number Newtonian flow. For example, experiments by V. Steinberg and collaborators have shown that dilute polymer suspensions being sheared in simple flow geometries can exhibit highly time dependent dynamics and show efficient mixing. The corresponding experiments using Newtonian fluids do not, and indeed cannot, show such nontrivial dynamics. To better understand these phenomena we study numerically the 2D Oldroyd-B Viscoelastic model at low Reynolds number. A background force is used to create a periodic cell with four-roll mill vortical structure around a hyperbolic fixed point. We consider both steady and time-periodic forcing. For low Weissenberg number (Wi) the elastic stresses are bounded and slave to the forcing, with mixing confined to small sets near the hyperbolic point. At larger Wi an analog to the coil-stretch transition occurs yielding large stresses and stress gradients concentrated on sets of small measure, perhaps indicating the development of singularities. The flow then becomes very sensitive to perturbations in the forcing and there is a transition to global mixing in the fluid.